U.S. digital cellular (USDC) communications uses digitized voice and data signals for communication between a mobile telephone and a base station. The mobiles and bases employ time division multiple access (TDMA) modulation for the transmission of these signals. A typical format for the TDMA data bursts is illustrated in FIG. 5. This data burst, as well as USDC in general, is discussed in more detail in the USDC specification EIA/TIA IS-54 available from Electronic Industries Association, Engineering Department, 2001 Eye Street, N.W., Washington, D.C. 20006.
When the mobile moves, it may encounter degraded communication channels due to noise and multipath distortion; both noise and distortion varying with time. The multipath distortion is due to a signal being received by the mobile at different times when it bounces off buildings and terrain. Multipath channels can cause inter-symbol interference (ISI) that can be removed with an adaptive channel equalizer, a specific type of adaptive filter. An adaptive channel estimator is another type of adaptive filter.
A typical adaptive filter is illustrated in FIG. 1. The input signal (106) is processed by the adaptive filter (101), producing the adaptive filter output signal (102). The output of the filter is then subtracted (105) from a reference signal (103), typically the unfiltered input signal (106), to produce an error signal (104). This error signal (104) is used by an adaptive algorithm with an update coefficient, .mu., in the adaptive filter to update the filter coefficients. The update coefficient is also referred to as a tracking coefficient or memory coefficient. The memory of the adaptive algorithm increases as the value of .mu. increases.
The adaptive algorithm may be a Kalman, Recursive Least Square, or Least Mean Square (LMS) algorithm. The typical goal of the adaptive algorithm is to minimize the mean square value of the error signal (104), fixed update coefficient. This value is typically designated mean square error (MSE).
A detrimental characteristic of adaptive channel equalizers is that they can experience degraded performance in the presence of a frequency offset of more than approximately 10 Hz (in a system with a 24 kHz symbol rate). While the specification for a transmission system requires a certain frequency variation limit, the adaptive channel equalizer may require a stricter limit. An example is the USDC system. USDC requires the receiver operating frequency to be locked within 200 Hz of the transmitter. The adaptive channel equalizer will not perform properly in this environment. A coarse automatic frequency control (AFC) is typically used to remove most of the offset. Any remaining offset, however, can detrimentally affect a detection algorithm and increase the detected bit error rate. There is a resulting need for an AFC that can reduce the frequency offset to an acceptably small level and track any variation of the offset as the environment changes when the mobile moves.